DSGE models and the obsession with Euler equations (wonkish)

3 Aug, 2014 at 15:35 | Posted in Economics | 9 Comments

In a post on his blog, sorta-kinda “New Keynesian” Paul Krugman argues that the problem with the academic profession is that some macroeconomists aren’t “bothered to actually figure out” how the New Keynesian model with its Euler conditions —  “based on the assumption that people have perfect access to capital markets, so that they can borrow and lend at the same rate” — really works. According to Krugman, this shouldn’t  be hard at all — “at least it shouldn’t be for anyone with a graduate training in economics.”

Hmm …

If people (not the representative agent) at least sometimes can’t help being off their labour supply curve — as in the real world — then what are these hordes of Euler equations that you find ad nauseam in “New Keynesian” macromodels gonna help us?

It is clear that the New Keynesian model, even extended to allow, say, for presence of investment and capital accumulation, or for the presence of both discrete price and nominal wage setting, is still just a toy model, and that it lacks many of the details which might be needed to understand fluctuations …

One striking (and unpleasant) characteristic of the basic New Keynesian model is that there is no unemployment! Movements take place along a labor supply curve, either at the intensive margin (with workers varying hours) or at the extensive margin (with workers deciding whether or not to participate). One has a sense, however, that this may give a misleading description of fluctuations, in positive terms, and, even more so, in normative terms: The welfare cost of fluctuations is often thought to fall disproportionately on the unemployed.

Olivier Blanchard

Yours truly’s doubts regarding the DSGE modelers’ obsession with Euler equations is basically that, as with so many other assumptions in ‘modern’ macroeconomics, the Euler equations don’t fit reality — and it seems as though I’m not alone holding that view:

For the uninitiated, the Consumption Euler Equation is sort of like the Flux Capacitor that powers all modern “DSGE” macro models … Basically, it says that how much you decide to consume today vs. tomorrow is determined by the interest rate (which is how much you get paid to put off your consumption til tomorrow), the time preference rate (which is how impatient you are) and your expected marginal utility of consumption (which is your desire to consume in the first place). When the equation appears in a macro model, “you” typically means “the entire economy”.

This equation underlies every DSGE model you’ll ever see, and drives much of modern macro’s idea of how the economy works. So why is Eichenbaum, one of the deans of modern macro, pooh-poohing it?

Simple: Because it doesn’t fit the data. The thing is, we can measure people’s consumption, and we can measure interest rates. If we make an assumption about people’s preferences, we can just go see if the Euler Equation is right or not!

[Martin] Eichenbaum was kind enough to refer me to the literature that tries to compare the Euler Equation to the data. The classic paper is Hansen and Singleton (1982), which found little support for the equation. But Eichenbaum also pointed me to this 2006 paper by Canzoneri, Cumby, and Diba of Georgetown (published version here), which provides simpler but more damning evidence against the Euler Equation …

[T]he Euler Equation says that if interest rates are high, you put off consumption more. That makes sense, right? Money markets basically pay you not to consume today. The more they pay you, the more you should keep your money in the money market and wait to consume until tomorrow.

But what Canzoneri et al. show is that this is not how people behave. The times when interest rates are high are times when people tend to be consuming more, not less.

OK, but what about that little assumption that we know people’s preferences? What if we’ve simply put the wrong utility function into the Euler Equation? Could this explain why people consume more during times when interest rates are high?

Well, Canzoneri et al. try out other utility functions that have become popular in recent years. The most popular alternative is habit formation … But when Canzoneri et al. put in habit formation, they find that the Euler Equation still contradicts the data …

Canzoneri et al. experiment with other types of preferences, including the other most popular alternative … No matter what we assume that people want, their behavior is not consistent with the Euler Equation …

If this paper is right … then essentially all modern DSGE-type macro models currently in use are suspect. The consumption Euler Equation is an important part of nearly any such model, and if it’s just wrong, it’s hard to see how those models will work.

Noah Smith

 

In the standard neoclassical consumption model — used in DSGE macroeconomic modeling — people are basically portrayed as treating time as a dichotomous phenomenon – today and the future — when contemplating making decisions and acting. How much should one consume today and how much in the future? Facing an intertemporal budget constraint of the form

c_t + c_f/(1+r) = f_t + y_t + y_f/(1+r),

where c_t is consumption today, c_f is consumption in the future, f_t is holdings of financial assets today, y_t is labour incomes today, y_f is labour incomes in the future, and r is the real interest rate, and having a lifetime utility function of the form

U = u(c_t) + au(c_f),

where a is the time discounting parameter, the representative agent (consumer) maximizes his utility when

u´(c_t) = a(1+r)u´(c_f).

This expression – the Euler equation – implies that the representative agent (consumer) is indifferent between consuming one more unit today or instead consuming it tomorrow. Typically using a logarithmic function form – u(c) = log c – which gives u´(c) = 1/c, the Euler equation can be rewritten as

1/c_t = a(1+r)(1/c_f),

or

c_f/c_t = a(1+r).

This importantly implies that according to the neoclassical consumption model that changes in the (real) interest rate and the ratio between future and present consumption move in the same direction.

So good, so far. But how about the real world? Is the neoclassical consumption as described in this kind of models in tune with the empirical facts? Hardly — the data and models are as a rule insconsistent!

In the Euler equation we only have one interest rate,  equated to the money market rate as set by the central bank. The crux is that — given almost any specification of the utility function  – the two rates are actually often found to be strongly negatively correlated in the empirical literature:

 In this paper, we use U.S. data to calculate the interest rate implied by the Euler equation, and we compare this Euler equation rate with a money market rate. We find the behavior of the money market rate differs significantly from the implied Euler equation rate. This poses a fundamental challenge for models that equate the two rates.

The fact that the two interest rate series do not coincide – and that the spread between the Euler equation rate and the money market rate is generally positive – comes as no surprise; these anomalies have been well documented in the literature on the “equity premium puzzle” and the “risk free rate puzzle.” And the failure of consumption Euler equation models should come as no surprise; there is a sizable literature that tries to fit Euler equations, and generally finds that the data on returns and aggregate consumption are not consistent with the model.

If the spread between the two rates were simply a constant, or a constant plus a little statistical noise, then the problem might not be thought to be very serious. The purpose of this paper is to document something more fundamental – and more problematic – in the relationship between the Euler equation rate and observed money market rates … We compute the implied Euler equation rates for a number of specifications of preferences and find that they are strongly negatively correlated with money market rates …

Our results suggest that the problem is fundamental: alternative specifications of preferences can eliminate the excessive volatility, but they yield an Euler equation rate that is strongly negatively correlated with the money market rate.

Matthew Canzoneri, Robert Cumby and Behzad Diba

Well, that more or less says it all, doesn’t it?